Controllers are supposed to coordinate the interactions between views and models by propagating changes and events between the two.
For example, if you had a todosController responsible for controlling a collection of views, there isn't really a clean way (in my opinion) to utilize it from two independent Backbone views without passing the controller through to the view (which makes the view depend on the controller). By handling events in the controller instead of in the view, you remove this dependency (which is also similar to my perception of Cocoa's delegates/SproutCore's bindings, but I may be wrong).
Both Spine's and Backbone's view layer consists of rendering templates to the DOM. To me, a "proper" view layer would include things like positioning and both frameworks seem to utilize CSS to do this, for the most part.
I think of Backbone's controllers as a poor man's State chart, without any enter or exit callbacks (e.g going from "#/" to "#/todos" should trigger a callback that states that I will exit the state "#/", so I can do necessary cleanup).